This paper introduces a computational model of creative problem solving in deep reinforcement learning agents, inspired by cognitive theories of creativity. The AIGenC model aims at enabling artificial agents to learn, use and generate transferable representations. AIGenC is embedded in a deep learning architecture that includes three main components: concept processing, reflective reasoning, and blending of concepts. The first component extracts objects and affordances from sensory input and encodes them in a concept space, represented as a hierarchical graph structure. Concept representations are stored in a dual memory system. Goal-directed and temporal information acquired by the agent during deep reinforcement learning enriches the representations creating a higher-level of abstraction in the concept space. In parallel, a process akin to reflective reasoning detects and recovers from memory concepts relevant to the task according to a matching process that calculates a similarity value between the current state and memory graph structures. Once an interaction is finalised, rewards and temporal information are added to the graph structure, creating a higher abstraction level. If reflective reasoning fails to offer a suitable solution, a blending process comes into place to create new concepts by combining past information. We discuss the model's capability to yield better out-of-distribution generalisation in artificial agents, thus advancing toward artificial general intelligence. To the best of our knowledge, this is the first computational model, beyond mere formal theories, that posits a solution to creative problem solving within a deep learning architecture.